A numerical investigation on evaporating spray with a turbulent air crossflow was presented to understand the mixing
characteristics of the water vapor and the crossflow. The numerical simulation was conducted upon a horizontal tube. Four
pressure swirl nozzles, which were evenly mounted in the same cross section of the tube, were used to inject spray droplets
into the air crossflow. Two-way coupling between the continuous phase and dispersed phase was considered. Different nozzle
injection modes were investigated in an attempt to discover the desired injection mode that leads to optimum mixing effect and
maximum temperature drop along the tube. A new formulation of degree of mixedness was proposed to assess the mixing
effect of the evaporating spray and the crossflow. The results show that under the condition of axial injection mode, the flow
structure, average temperature distribution and degree of mixedness demonstrate similar variation tendency with the
evaporation of droplets and development of mixing along the crossflow. Counter-rotating vortex pairs appear due to the
disturbance of spray droplets and promote the mixing performance to some extent. A small tangential injection angle, 5°,
provides optimal mixing effect as a result of large vortex instead of counter-rotating vortex pairs in the cross section of the
tube. Moreover, unbiased injection mode results in considerable temperature drop along the tube.

General Note:

The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows

A numerical investigation on evaporating spray with a turbulent air crossflow was presented to understand the mixing
characteristics of the water vapor and the crossflow. The numerical simulation was conducted upon a horizontal tube. Four
pressure swirl nozzles, which were evenly mounted in the same cross section of the tube, were used to inject spray droplets
into the air crossflow. Two-way coupling between the continuous phase and dispersed phase was considered. Different nozzle
injection modes were investigated in an attempt to discover the desired injection mode that leads to optimum mixing effect and
maximum temperature drop along the tube. A new formulation of degree of mixedness was proposed to assess the mixing
effect of the evaporating spray and the crossflow. The results show that under the condition of axial injection mode, the flow
structure, average temperature distribution and degree of mixedness demonstrate similar variation tendency with the
evaporation of droplets and development of mixing along the crossflow. Counter-rotating vortex pairs appear due to the
disturbance of spray droplets and promote the mixing performance to some extent. A small tangential injection angle, 5,
provides optimal mixing effect as a result of large vortex instead of counter-rotating vortex pairs in the cross section of the
tube. Moreover, unbiased injection mode results in considerable temperature drop along the tube.

Introduction

Water spray is traditionally applied in the fields of fire
extinguishment, humidifying, cooling, food processing, etc.
In recent years, water spray finds its new promising
application in underwater propulsion system, in particular,
water ramjet system. In the mixing chamber of water ramjet,
the water is injected by the nozzles to the main crossflow
discharged from the combustion chamber. The spray
evaporates in the influence of the crossflow at high
temperature and then the vapor mixes with the crossflow.
On one hand, water spray can assist to decrease the
temperature of the fuel gas from the combustion chamber;
on the other hand, the addition of water spray contributes to
the increase of the working substance of the nozzle at the
end of the water ramjet. A large temperature drop and good
mixing effects play an important role on the thrust of the
water ramjet. Therefore, it is necessary to investigate the
mixing characteristics under the influence of different
factors in order to discover the role and mechanism.
Since the mixing process is dominant in water ramjet, the
present study concentrates on the mixing characteristics of
evaporating spray droplets and crossflow. Generally, the
objective is to obtain a homogeneous mixture of the
injectant and mainstream (Liscinsky et al., 1996). Many
researches have been reported regarding the mixing process
in gas turbine combustor, solid and liquid rocket motor, etc.
Evaluation and enhancement of the performance of the

mixing section for the combustor concept,
Rich-burn/Quick-mix/Lean-burn (RQL), has been the
subject of many experimental and numerical studies of
crossflow mixing (Holdeman 1993; Liscinsky et al., 1994;
Holdeman et al., 1997; Everson et al., 1998; Leong et al.,
2000). In the gas turbine combustor, Holdeman (1993)
proposed that the most important design parameters were
jet-to-mainstream momentum-flux ratio and orifice
spacing-to-duct height ratio. In other researches, the
arrangement method of orifices is usually the hot research
subject because it significantly influences the distribution of
jet flow and mainstream. However, the studies on the
mixing process in water ramjet are much less than in the
above motors. In this type of motor, the water jet is usually
sprayed into droplets by the centrifugal nozzles and then the
droplets are heated into vapour by the hot crossflow. The
factors influencing the temperature drop and the mixing
characteristics include the ratio of mass flow of spray and
crossflow, the initial temperature of the spray and the
crossflow, the spray angle, the initial diameter of the spray
droplets, the velocity difference between the spray droplets
and the crossflow, the number of the nozzle and the nozzle
injection mode, etc.
The heat and mass transfer between the spray and main
stream is the classical research subject in multiphase flow.
Kachhwaha et al. (1997) developed a simple and efficient
numerical model for estimation of heat and mass transfer
between water spray droplets and an air stream in horizontal

parallel flow and counter flow configuration. Barata et al.
(2005) evaluated and improved an Eulerian/Lagrangian
approach to account for turbulent dispersion, evaporation
and coupling between both processes in spray systems. It
was extended to the case of an array of evaporating droplets
through a crossflow and the result was found to be strongly
dependent on the evaporation models used. Wang et al.
(2007) simulated the humidifying process involving
two-phase flow of air and water droplets in the counter-flow
spray saturator for humid air turbine cycle. Moukalled et al.
(2008) tested three numerical techniques based on a full
multiphase approach, a multisize-group (MUSIG) approach
and a heterogeneous MUSIG (H-MUSIG) approach for the
prediction of mixing and evaporation of liquid droplets
injected into a stream of air at all speeds. Different from
above researches, this work try to provide a new perspective
to investigate the spray and crossflow system.
In our recent experiment (Bai et al., 2009), the injection
mode of the nozzles was considered as one important factor
affecting the mixing effect in the turbulent mixing of
non-evaporating spray droplets and crossflow. The present
work will focus on the influence of nozzle injection modes
on the mixing characteristics of evaporating spray and
crossflow. Moreover, a new formulation of degree of
mixedness will be proposed to quantitatively evaluate the
mixing effect. Consequently, the optimum arrangement of
the nozzles will be obtained to provide theoretical basis for
the performance optimization of the water ramjet system.

Regarding the simulation of gas-droplets two-phase flow
in the tube, the crossflow is treated as continuous phase,
transport equations of which are solved using the Eulerian
approach. The spray droplets are treated as dispersed phase,
transport equations of which are solved using the
Lagrangian approach.

Gas phase equations

The gas flow equations consist of the conservation for
mass, momentum, energy and concentration for one
continuous phase. The realizable k-s model is applied to
characterize the turbulence effect. All the governing
equations can be unified as
a a a +
(pu )= c (F )+S, +SF (1)
In equation (1), 0 represents the dependent variable, 1, v, H,
C, k and e.
The gas phase equations are solved numerically using a
control-volume technique embodied in the SIMPLE
algorithm.

Dispersed phase equations

The formation of the liquid film, the breakup process of
sheet and the generation of droplets aren't taken into
account while the hollow cone spray shape and the Sauter
diameter of the droplets are concerned. The pressure-swirl
spray model, named as the linearized instability sheet
atomization (LISA) model of Schmidt et al.(1999), is
applied to add droplets into the crossflow. The atomization
process involves breakup, collision, and coalescence of
droplets. The well known TAB breakup model (O'Rourke et
al., 1987) is used, which is suitable for predicting the
secondary breakup regime in the jet process with low We
number. O'Rourke statistical particle method (O'Rourke
1989), for which parcels of droplets are tracked

Paper No

Paper No

simultaneously in three-dimensional space and with time, is
used to simulate the collision and coalescence process of
droplets.
The droplet trajectories are calculated in Lagrangian
framework. The forces acting on the droplets generally
include aerodynamic drag, gravitation, added mass, gas
phase pressure gradient, Basset history integral, Saffman
and Magnus lift force. The Basset force acting on the
particles in the turbulent flow can be ignored. The Saffman
and Magnus lift force can also be neglected in the case of
small velocity gradient in the main flow (Liu et al., 1996).
Furthermore, the forces except drag and volume forces are
negligible when the gas/particle density ratio is smaller than
10-3 (Crowe et al., 1996). Therefore, aerodynamic drag and
gravitation are considered to be non-negligible. The droplets
are assumed to be spherical. The motion of the droplets is
described by

dup
dt (u up) / rp + g
2 4 ,D2
S 24pLD
S18/CDRep

-P Pglug uplD

CD 24 (1+0.15Re0687) (Re<1000)

CD =0.44 (Rep1000)

The turbulence effect is simulated using the stochastic
droplet tracking method, in which the instantaneous velocity
of gas phase is decomposed into a mean and fluctuating
component
u = u + u (6)
where, u is determined through solving gas phase equations
and u'is sampled randomly from a Gaussian probability
distribution of gas phase velocity.
The momentum change of a droplet as it passes through
each control volume is computed as
18CDPg
F Z= (ug up,)rpAt (7)
24pp D
This momentum exchange appears as a momentum sink in
the continuous phase momentum balance.
The rate of vaporization is given by
h = -27cgDgDpSh ln(1 +B,) (8)

1,1
rh= -2I DpNu ln(1+BT) (9)
pg
Sh= 2+0.6Rel/2Sc'/3 (10)
Nu = 2 + 0.6Re/2Pr1/3 (11)
Assuming that Le=l, the heat transfer rate is equal to the
mass transfer rate, so equations (8) and (9) are equivalent.
The droplet's temperature is obtained via the heat balance
of the convective and latent heat transfer
dT 6 /x L mc t
S-- x (T T)Nu +-T- (7)
dt Dpc, L cp,g
The mass exchange as a source of mass in the continuity
equation and also a source of species for water vapor of the
continuous phase is computed as

The simplified geometry structure of the mixing chamber
(2) and the computational domain are shown in Fig.l. The
simulation is conducted in a horizontal tube with a length of
(3) 500mm and inner diameter of 95mm. Four pressure swirl
nozzles are mounted on the same cross section of the tube
with a 100mm distance from the inlet. The hollow cone
(4) spray is injected by the swirl nozzles into the tube and then
the spray droplets evaporate in the hot crossflow. The
symbols in Fig.1, a and /, denote the axial and tangential
injection angle of the nozzle respectively.

Since few data in the previous studies can be found
related to the present research, the present numerical
algorithm and computed results are validated by comparing
the simulated results with the experiment results conducted
by the authors. The experiment was carried out in a
rectangular duct with cross section size of 95x95mm. The
crossflow material was air with inlet temperature of 673K
and inlet velocity of 30m/s. One nozzle instead of four
nozzles was used. The spray material was acetone with mass
flow rate of 0.001kg/s, initial temperature of 284K, initial
Sauter diameter of 48gm, and spray angle of 800. Figure 2
shows the temperature drop in half of the cross sections
along the duct. The two sub figures illustrate that the
simulation results agree well with the experiment ones.
Based on the validation, we can further proceed with the
simulation.

The influences of injection modes of nozzles on mixing
characteristics of evaporating spray with crossflow are
assessed by two main parameters, the degree of mixedness
and the temperature drop. The quantitative index for
mixing, degree of mixedness, is proposed as
Sn min X -X + max X, X
= = Y (13)
n,1 |X-X +max X,-X|
1l<
In equation (13), X is the parameter of interest, which
can be temperature and mass fraction of one of the species
in continuous flow, et al. The cross section is divided into n
small regions, and X, means the value of region i. X is
the average value. The degree of mixedness is bounded
between 0 and 1. The higher value indicates the more
desirable mixing effect.
In this work, temperature is used to calculate the degree
of mixedness.

Figure 3, 4, 5, and 6 show the temperature distribution,
flow structure and mixing effect with different axial
injection angles including 600, 800, 900, 1000 and 1200. It
can be observed from Fig.3 that axial injection mode does
not show distinct superiority in bringing about large
temperature drop. Instead, unbiased injection (900) can
cause considerable temperature drop. The degree of
mixedness reflects the uniformity of temperature in the
cross section. It undergoes similar variation tendency
under different axial injection angles. In near-nozzle region
(e.g. x=120mm in Fig.5), though the temperature in the
cross section seems high, the temperature distribution is
relatively even. Therefore, the degree of mixedness
reaches a relatively high value in a short distance.
However, with the evaporation of droplets and the increase
of mixing distance, the degree of mixedness will suffer
some degree of decrease. It is due to the increase of the
temperature difference in the cross section (e.g. x=500mm
in Fig.5). As Fig.4 shows, the degrees of mixedness at the
outlet of the tube under different axial injection angles
approximate to each other. Moreover, the flow structures
under different conditions are similar, too. It is obvious in
Fig.6 that counter-rotating vortex pairs (CVPs) appear in
the cross section. The CVP was regarded as the main
reason influencing the mixing effect in the cold state
experiment without considering the evaporation of droplets
(Bai et al., 2009). The CVPs also occur in the mixing with
the evaporation of spray droplets and improve the mixing
of different components to some extent. However, with the
increase of a, the penetration depth of the spray to the
crossflow decreases, leading to weak disturbance. When
a=1200, the CVPs tend to fade compared to other
conditions (see Fig.6 (j)).

Figure 7, 8, 9, and 10 show the temperature distribution,
flow structure and mixing effect under different tangential
injection angles including 50, 100, 200. Actually, the
tangential injection angle of 00 occurs at the same

condition as the axial injection angle of 900 does in this
study, that is, they refer to the unbiased injection. Similar
to the axial injection mode, as Fig.7 shows, the unbiased
injection (0) provide substantial temperature drop.
Although the tangential injection angle of 50 and 100 could
not bring about satisfying temperature drop, they provide
good mixing effect (see Fig.8). It can be observed from
Fig.9 (b) that the temperature is slightly different from
region to region in the outlet cross section (x=500mm).The
flow structures in Fig. 10 for the tangential injection angles
of 50 and 100 are different from that for the tangential
injection angles of 00 and 200. Large vortex appears in the
cross section for the former two cases, and as a result the
large vortex is in favour of mixing. It can be deduced that
the slightly tangential injection is beneficial to obtain
optimal mixing.

0.1 0.2 0.3 0.4 0.5
x[m]
Fig. 7: Average temperature in the cross sections under
different tangential injection angles of the nozzles.

900, 1000 and 1200, the tangential injection angles of
nozzles involving 50, 100 and 200 and unbiased nozzle
injection were investigated in order to discover favourable
injection modes that optimize mixing effect and maximize
temperature drop as well. The unbiased injection provide
large average temperature drop. However, the slightly
tangential injection brings about optimal mixing effect. The
average temperature and degree of mixedness in the cross
section show similar variation tendency under different axial
injection angles. The counter-rotating vortex pairs occur due
to the disturbance of spray droplets and promote the mixing
performance to some extent. Large vortex appears when the
tangential injection angles are 50 and 100, and consequently
the optimal mixing effect is obtained due to the onset of
large vortex.
The crossflow velocity in this paper is the same value
under different nozzle injection modes. Since the relative
velocity between the spray droplets and crossflow greatly
influences the droplets evaporation, we speculate that the
nozzle injection modes will exert different influences on the
mixing performance at different crossflow velocity. It will
be further investigated in the followup research.

Acknowledgements

The present work was financially supported by the
National Nature Science Foundation of China for Creative
Research Groups under the Contract No. 50821604.